Exercise #3: A function rule takes an input, n, and converts it into an output, $, by increasing one half of the
input by 10. Determine the output for this rule when the input is 50 and then write an equation for the rule.

Let x have probability generating function gx (s) and let un generating function u(s) of the sequence uo, u1, satisfies p(x > n). show that the (1- s)u(s) = 1 - gx(s), whenever the series defining these generating functions converge.